OK, finally someone who seems to have it together to be able to play.
I'll get your feet wet and start here:
Ceiling Fand wiring Diagrams
and:
CeilingFanParts.com Home
One of the first things you have to do, is find out what the configuration of the capacitor is. 3 wire is pretty easy to deal with.
In an integrated speed control, I don't know if the caps are in the speed control or in the fan. Suspect fan because they are big components.
An add on speed control generally wants you to set the unit to the fastest speed.
In order not to burn things up, you can use fuses or even a 60 W light bub in series with things.
So, you can write everything down for starters and try to identify the windings.
Decoding one of the schematics for you; 3 speed dual capacitor.
You can ignore the reversing switch for any initial tests. All it does is swap the polarity of one of the windings. Basically wired as a DPDT switch with the far ends crossed and the winding taken from the middle two terminals or one of the ends or vice versa. So, it's a simple 2 wire in with 2 wires out to an isolated winding. Just a lot of wires you don't need to concern yourself with initially.
The motor types is a PSC motor or a permanent split capacitor motor. The cap provides somewhat of a phase shift causing the motor to operate. The motors have crummy torque.
So, you have to identify the windings for starters and figure out which one gets the capacitor.
The speed control when a dual capacitor is used is just two caps with a one side common. Simple enough. What happens next is if the lowest value ca is used, you get the lowest speed. If the mid one is used, you get the middle speed.
Since capacitance adds when capacitors are in parallel, then the parallel combination is the highest value and thus the highest speed.
So, the switch that is used is/can be a simple A, B and A+B and off switched to line just like a 3-way lamp switch works, so again you have 2 terminals for the capacitor for this combination.
So you now have 2 windings (4 wires) and 2 wires for a capacitor (switch+dual cap) and power in.
When you try to cram all of this with the reversing switch, you have a mess. A fan reversing switch has tapped holes and this it's easier to install in the fan. When yo purchase the switch from the source given, it contains all the wires heat shrunk too.
The reversing switch really isn't rated to just move when you feel like it. The fan should be stopped and you'll have no problems.
Now, I suspect the other speed control switches may use different combinations of the capacitors to change speed. Remember that capacitors in series behave like 1/Ct=1/C1+1/C2... +1/Cn and caps in parallel behave like Ct = C1 + C2 +... Cn; opposite from resistors.
You'll have to do the leg work, but I can help if I can. You don't need the blades, the lamps or the reversing switch or even the speed switch to start.
I identify and add incrementally and you really should be fine.
Then you can tell all of us about it.
Deal?
KISS
PS: You need way too many wires for the capacitor thing/reverse to work.